tjh.dev
Linux kernel mirror (for testing)
git.kernel.org/pub/scm/linux/kernel/git/torvalds/linux.git
kernel
os
linux
1/*
2 * ECC algorithm for M-systems disk on chip. We use the excellent Reed
3 * Solmon code of Phil Karn (karn@ka9q.ampr.org) available under the
4 * GNU GPL License. The rest is simply to convert the disk on chip
5 * syndrom into a standard syndom.
6 *
7 * Author: Fabrice Bellard (fabrice.bellard@netgem.com)
8 * Copyright (C) 2000 Netgem S.A.
9 *
10 * $Id: docecc.c,v 1.7 2005/11/07 11:14:25 gleixner Exp $
11 *
12 * This program is free software; you can redistribute it and/or modify
13 * it under the terms of the GNU General Public License as published by
14 * the Free Software Foundation; either version 2 of the License, or
15 * (at your option) any later version.
16 *
17 * This program is distributed in the hope that it will be useful,
18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU General Public License for more details.
21 *
22 * You should have received a copy of the GNU General Public License
23 * along with this program; if not, write to the Free Software
24 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
25 */
26#include <linux/kernel.h>
27#include <linux/module.h>
28#include <asm/errno.h>
29#include <asm/io.h>
30#include <asm/uaccess.h>
31#include <linux/miscdevice.h>
32#include <linux/pci.h>
33#include <linux/delay.h>
34#include <linux/slab.h>
35#include <linux/sched.h>
36#include <linux/init.h>
37#include <linux/types.h>
38
39#include <linux/mtd/compatmac.h> /* for min() in older kernels */
40#include <linux/mtd/mtd.h>
41#include <linux/mtd/doc2000.h>
42
43#define DEBUG_ECC 0
44/* need to undef it (from asm/termbits.h) */
45#undef B0
46
47#define MM 10 /* Symbol size in bits */
48#define KK (1023-4) /* Number of data symbols per block */
49#define B0 510 /* First root of generator polynomial, alpha form */
50#define PRIM 1 /* power of alpha used to generate roots of generator poly */
51#define NN ((1 << MM) - 1)
52
53typedef unsigned short dtype;
54
55/* 1+x^3+x^10 */
56static const int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 };
57
58/* This defines the type used to store an element of the Galois Field
59 * used by the code. Make sure this is something larger than a char if
60 * if anything larger than GF(256) is used.
61 *
62 * Note: unsigned char will work up to GF(256) but int seems to run
63 * faster on the Pentium.
64 */
65typedef int gf;
66
67/* No legal value in index form represents zero, so
68 * we need a special value for this purpose
69 */
70#define A0 (NN)
71
72/* Compute x % NN, where NN is 2**MM - 1,
73 * without a slow divide
74 */
75static inline gf
76modnn(int x)
77{
78 while (x >= NN) {
79 x -= NN;
80 x = (x >> MM) + (x & NN);
81 }
82 return x;
83}
84
85#define CLEAR(a,n) {\
86int ci;\
87for(ci=(n)-1;ci >=0;ci--)\
88(a)[ci] = 0;\
89}
90
91#define COPY(a,b,n) {\
92int ci;\
93for(ci=(n)-1;ci >=0;ci--)\
94(a)[ci] = (b)[ci];\
95}
96
97#define COPYDOWN(a,b,n) {\
98int ci;\
99for(ci=(n)-1;ci >=0;ci--)\
100(a)[ci] = (b)[ci];\
101}
102
103#define Ldec 1
104
105/* generate GF(2**m) from the irreducible polynomial p(X) in Pp[0]..Pp[m]
106 lookup tables: index->polynomial form alpha_to[] contains j=alpha**i;
107 polynomial form -> index form index_of[j=alpha**i] = i
108 alpha=2 is the primitive element of GF(2**m)
109 HARI's COMMENT: (4/13/94) alpha_to[] can be used as follows:
110 Let @ represent the primitive element commonly called "alpha" that
111 is the root of the primitive polynomial p(x). Then in GF(2^m), for any
112 0 <= i <= 2^m-2,
113 @^i = a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
114 where the binary vector (a(0),a(1),a(2),...,a(m-1)) is the representation
115 of the integer "alpha_to[i]" with a(0) being the LSB and a(m-1) the MSB. Thus for
116 example the polynomial representation of @^5 would be given by the binary
117 representation of the integer "alpha_to[5]".
118 Similarily, index_of[] can be used as follows:
119 As above, let @ represent the primitive element of GF(2^m) that is
120 the root of the primitive polynomial p(x). In order to find the power
121 of @ (alpha) that has the polynomial representation
122 a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
123 we consider the integer "i" whose binary representation with a(0) being LSB
124 and a(m-1) MSB is (a(0),a(1),...,a(m-1)) and locate the entry
125 "index_of[i]". Now, @^index_of[i] is that element whose polynomial
126 representation is (a(0),a(1),a(2),...,a(m-1)).
127 NOTE:
128 The element alpha_to[2^m-1] = 0 always signifying that the
129 representation of "@^infinity" = 0 is (0,0,0,...,0).
130 Similarily, the element index_of[0] = A0 always signifying
131 that the power of alpha which has the polynomial representation
132 (0,0,...,0) is "infinity".
133
134*/
135
136static void
137generate_gf(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1])
138{
139 register int i, mask;
140
141 mask = 1;
142 Alpha_to[MM] = 0;
143 for (i = 0; i < MM; i++) {
144 Alpha_to[i] = mask;
145 Index_of[Alpha_to[i]] = i;
146 /* If Pp[i] == 1 then, term @^i occurs in poly-repr of @^MM */
147 if (Pp[i] != 0)
148 Alpha_to[MM] ^= mask; /* Bit-wise EXOR operation */
149 mask <<= 1; /* single left-shift */
150 }
151 Index_of[Alpha_to[MM]] = MM;
152 /*
153 * Have obtained poly-repr of @^MM. Poly-repr of @^(i+1) is given by
154 * poly-repr of @^i shifted left one-bit and accounting for any @^MM
155 * term that may occur when poly-repr of @^i is shifted.
156 */
157 mask >>= 1;
158 for (i = MM + 1; i < NN; i++) {
159 if (Alpha_to[i - 1] >= mask)
160 Alpha_to[i] = Alpha_to[MM] ^ ((Alpha_to[i - 1] ^ mask) << 1);
161 else
162 Alpha_to[i] = Alpha_to[i - 1] << 1;
163 Index_of[Alpha_to[i]] = i;
164 }
165 Index_of[0] = A0;
166 Alpha_to[NN] = 0;
167}
168
169/*
170 * Performs ERRORS+ERASURES decoding of RS codes. bb[] is the content
171 * of the feedback shift register after having processed the data and
172 * the ECC.
173 *
174 * Return number of symbols corrected, or -1 if codeword is illegal
175 * or uncorrectable. If eras_pos is non-null, the detected error locations
176 * are written back. NOTE! This array must be at least NN-KK elements long.
177 * The corrected data are written in eras_val[]. They must be xor with the data
178 * to retrieve the correct data : data[erase_pos[i]] ^= erase_val[i] .
179 *
180 * First "no_eras" erasures are declared by the calling program. Then, the
181 * maximum # of errors correctable is t_after_eras = floor((NN-KK-no_eras)/2).
182 * If the number of channel errors is not greater than "t_after_eras" the
183 * transmitted codeword will be recovered. Details of algorithm can be found
184 * in R. Blahut's "Theory ... of Error-Correcting Codes".
185
186 * Warning: the eras_pos[] array must not contain duplicate entries; decoder failure
187 * will result. The decoder *could* check for this condition, but it would involve
188 * extra time on every decoding operation.
189 * */
190static int
191eras_dec_rs(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1],
192 gf bb[NN - KK + 1], gf eras_val[NN-KK], int eras_pos[NN-KK],
193 int no_eras)
194{
195 int deg_lambda, el, deg_omega;
196 int i, j, r,k;
197 gf u,q,tmp,num1,num2,den,discr_r;
198 gf lambda[NN-KK + 1], s[NN-KK + 1]; /* Err+Eras Locator poly
199 * and syndrome poly */
200 gf b[NN-KK + 1], t[NN-KK + 1], omega[NN-KK + 1];
201 gf root[NN-KK], reg[NN-KK + 1], loc[NN-KK];
202 int syn_error, count;
203
204 syn_error = 0;
205 for(i=0;i<NN-KK;i++)
206 syn_error |= bb[i];
207
208 if (!syn_error) {
209 /* if remainder is zero, data[] is a codeword and there are no
210 * errors to correct. So return data[] unmodified
211 */
212 count = 0;
213 goto finish;
214 }
215
216 for(i=1;i<=NN-KK;i++){
217 s[i] = bb[0];
218 }
219 for(j=1;j<NN-KK;j++){
220 if(bb[j] == 0)
221 continue;
222 tmp = Index_of[bb[j]];
223
224 for(i=1;i<=NN-KK;i++)
225 s[i] ^= Alpha_to[modnn(tmp + (B0+i-1)*PRIM*j)];
226 }
227
228 /* undo the feedback register implicit multiplication and convert
229 syndromes to index form */
230
231 for(i=1;i<=NN-KK;i++) {
232 tmp = Index_of[s[i]];
233 if (tmp != A0)
234 tmp = modnn(tmp + 2 * KK * (B0+i-1)*PRIM);
235 s[i] = tmp;
236 }
237
238 CLEAR(&lambda[1],NN-KK);
239 lambda[0] = 1;
240
241 if (no_eras > 0) {
242 /* Init lambda to be the erasure locator polynomial */
243 lambda[1] = Alpha_to[modnn(PRIM * eras_pos[0])];
244 for (i = 1; i < no_eras; i++) {
245 u = modnn(PRIM*eras_pos[i]);
246 for (j = i+1; j > 0; j--) {
247 tmp = Index_of[lambda[j - 1]];
248 if(tmp != A0)
249 lambda[j] ^= Alpha_to[modnn(u + tmp)];
250 }
251 }
252#if DEBUG_ECC >= 1
253 /* Test code that verifies the erasure locator polynomial just constructed
254 Needed only for decoder debugging. */
255
256 /* find roots of the erasure location polynomial */
257 for(i=1;i<=no_eras;i++)
258 reg[i] = Index_of[lambda[i]];
259 count = 0;
260 for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {
261 q = 1;
262 for (j = 1; j <= no_eras; j++)
263 if (reg[j] != A0) {
264 reg[j] = modnn(reg[j] + j);
265 q ^= Alpha_to[reg[j]];
266 }
267 if (q != 0)
268 continue;
269 /* store root and error location number indices */
270 root[count] = i;
271 loc[count] = k;
272 count++;
273 }
274 if (count != no_eras) {
275 printf("\n lambda(x) is WRONG\n");
276 count = -1;
277 goto finish;
278 }
279#if DEBUG_ECC >= 2
280 printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
281 for (i = 0; i < count; i++)
282 printf("%d ", loc[i]);
283 printf("\n");
284#endif
285#endif
286 }
287 for(i=0;i<NN-KK+1;i++)
288 b[i] = Index_of[lambda[i]];
289
290 /*
291 * Begin Berlekamp-Massey algorithm to determine error+erasure
292 * locator polynomial
293 */
294 r = no_eras;
295 el = no_eras;
296 while (++r <= NN-KK) { /* r is the step number */
297 /* Compute discrepancy at the r-th step in poly-form */
298 discr_r = 0;
299 for (i = 0; i < r; i++){
300 if ((lambda[i] != 0) && (s[r - i] != A0)) {
301 discr_r ^= Alpha_to[modnn(Index_of[lambda[i]] + s[r - i])];
302 }
303 }
304 discr_r = Index_of[discr_r]; /* Index form */
305 if (discr_r == A0) {
306 /* 2 lines below: B(x) <-- x*B(x) */
307 COPYDOWN(&b[1],b,NN-KK);
308 b[0] = A0;
309 } else {
310 /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
311 t[0] = lambda[0];
312 for (i = 0 ; i < NN-KK; i++) {
313 if(b[i] != A0)
314 t[i+1] = lambda[i+1] ^ Alpha_to[modnn(discr_r + b[i])];
315 else
316 t[i+1] = lambda[i+1];
317 }
318 if (2 * el <= r + no_eras - 1) {
319 el = r + no_eras - el;
320 /*
321 * 2 lines below: B(x) <-- inv(discr_r) *
322 * lambda(x)
323 */
324 for (i = 0; i <= NN-KK; i++)
325 b[i] = (lambda[i] == 0) ? A0 : modnn(Index_of[lambda[i]] - discr_r + NN);
326 } else {
327 /* 2 lines below: B(x) <-- x*B(x) */
328 COPYDOWN(&b[1],b,NN-KK);
329 b[0] = A0;
330 }
331 COPY(lambda,t,NN-KK+1);
332 }
333 }
334
335 /* Convert lambda to index form and compute deg(lambda(x)) */
336 deg_lambda = 0;
337 for(i=0;i<NN-KK+1;i++){
338 lambda[i] = Index_of[lambda[i]];
339 if(lambda[i] != A0)
340 deg_lambda = i;
341 }
342 /*
343 * Find roots of the error+erasure locator polynomial by Chien
344 * Search
345 */
346 COPY(®[1],&lambda[1],NN-KK);
347 count = 0; /* Number of roots of lambda(x) */
348 for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {
349 q = 1;
350 for (j = deg_lambda; j > 0; j--){
351 if (reg[j] != A0) {
352 reg[j] = modnn(reg[j] + j);
353 q ^= Alpha_to[reg[j]];
354 }
355 }
356 if (q != 0)
357 continue;
358 /* store root (index-form) and error location number */
359 root[count] = i;
360 loc[count] = k;
361 /* If we've already found max possible roots,
362 * abort the search to save time
363 */
364 if(++count == deg_lambda)
365 break;
366 }
367 if (deg_lambda != count) {
368 /*
369 * deg(lambda) unequal to number of roots => uncorrectable
370 * error detected
371 */
372 count = -1;
373 goto finish;
374 }
375 /*
376 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
377 * x**(NN-KK)). in index form. Also find deg(omega).
378 */
379 deg_omega = 0;
380 for (i = 0; i < NN-KK;i++){
381 tmp = 0;
382 j = (deg_lambda < i) ? deg_lambda : i;
383 for(;j >= 0; j--){
384 if ((s[i + 1 - j] != A0) && (lambda[j] != A0))
385 tmp ^= Alpha_to[modnn(s[i + 1 - j] + lambda[j])];
386 }
387 if(tmp != 0)
388 deg_omega = i;
389 omega[i] = Index_of[tmp];
390 }
391 omega[NN-KK] = A0;
392
393 /*
394 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
395 * inv(X(l))**(B0-1) and den = lambda_pr(inv(X(l))) all in poly-form
396 */
397 for (j = count-1; j >=0; j--) {
398 num1 = 0;
399 for (i = deg_omega; i >= 0; i--) {
400 if (omega[i] != A0)
401 num1 ^= Alpha_to[modnn(omega[i] + i * root[j])];
402 }
403 num2 = Alpha_to[modnn(root[j] * (B0 - 1) + NN)];
404 den = 0;
405
406 /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
407 for (i = min(deg_lambda,NN-KK-1) & ~1; i >= 0; i -=2) {
408 if(lambda[i+1] != A0)
409 den ^= Alpha_to[modnn(lambda[i+1] + i * root[j])];
410 }
411 if (den == 0) {
412#if DEBUG_ECC >= 1
413 printf("\n ERROR: denominator = 0\n");
414#endif
415 /* Convert to dual- basis */
416 count = -1;
417 goto finish;
418 }
419 /* Apply error to data */
420 if (num1 != 0) {
421 eras_val[j] = Alpha_to[modnn(Index_of[num1] + Index_of[num2] + NN - Index_of[den])];
422 } else {
423 eras_val[j] = 0;
424 }
425 }
426 finish:
427 for(i=0;i<count;i++)
428 eras_pos[i] = loc[i];
429 return count;
430}
431
432/***************************************************************************/
433/* The DOC specific code begins here */
434
435#define SECTOR_SIZE 512
436/* The sector bytes are packed into NB_DATA MM bits words */
437#define NB_DATA (((SECTOR_SIZE + 1) * 8 + 6) / MM)
438
439/*
440 * Correct the errors in 'sector[]' by using 'ecc1[]' which is the
441 * content of the feedback shift register applyied to the sector and
442 * the ECC. Return the number of errors corrected (and correct them in
443 * sector), or -1 if error
444 */
445int doc_decode_ecc(unsigned char sector[SECTOR_SIZE], unsigned char ecc1[6])
446{
447 int parity, i, nb_errors;
448 gf bb[NN - KK + 1];
449 gf error_val[NN-KK];
450 int error_pos[NN-KK], pos, bitpos, index, val;
451 dtype *Alpha_to, *Index_of;
452
453 /* init log and exp tables here to save memory. However, it is slower */
454 Alpha_to = kmalloc((NN + 1) * sizeof(dtype), GFP_KERNEL);
455 if (!Alpha_to)
456 return -1;
457
458 Index_of = kmalloc((NN + 1) * sizeof(dtype), GFP_KERNEL);
459 if (!Index_of) {
460 kfree(Alpha_to);
461 return -1;
462 }
463
464 generate_gf(Alpha_to, Index_of);
465
466 parity = ecc1[1];
467
468 bb[0] = (ecc1[4] & 0xff) | ((ecc1[5] & 0x03) << 8);
469 bb[1] = ((ecc1[5] & 0xfc) >> 2) | ((ecc1[2] & 0x0f) << 6);
470 bb[2] = ((ecc1[2] & 0xf0) >> 4) | ((ecc1[3] & 0x3f) << 4);
471 bb[3] = ((ecc1[3] & 0xc0) >> 6) | ((ecc1[0] & 0xff) << 2);
472
473 nb_errors = eras_dec_rs(Alpha_to, Index_of, bb,
474 error_val, error_pos, 0);
475 if (nb_errors <= 0)
476 goto the_end;
477
478 /* correct the errors */
479 for(i=0;i<nb_errors;i++) {
480 pos = error_pos[i];
481 if (pos >= NB_DATA && pos < KK) {
482 nb_errors = -1;
483 goto the_end;
484 }
485 if (pos < NB_DATA) {
486 /* extract bit position (MSB first) */
487 pos = 10 * (NB_DATA - 1 - pos) - 6;
488 /* now correct the following 10 bits. At most two bytes
489 can be modified since pos is even */
490 index = (pos >> 3) ^ 1;
491 bitpos = pos & 7;
492 if ((index >= 0 && index < SECTOR_SIZE) ||
493 index == (SECTOR_SIZE + 1)) {
494 val = error_val[i] >> (2 + bitpos);
495 parity ^= val;
496 if (index < SECTOR_SIZE)
497 sector[index] ^= val;
498 }
499 index = ((pos >> 3) + 1) ^ 1;
500 bitpos = (bitpos + 10) & 7;
501 if (bitpos == 0)
502 bitpos = 8;
503 if ((index >= 0 && index < SECTOR_SIZE) ||
504 index == (SECTOR_SIZE + 1)) {
505 val = error_val[i] << (8 - bitpos);
506 parity ^= val;
507 if (index < SECTOR_SIZE)
508 sector[index] ^= val;
509 }
510 }
511 }
512
513 /* use parity to test extra errors */
514 if ((parity & 0xff) != 0)
515 nb_errors = -1;
516
517 the_end:
518 kfree(Alpha_to);
519 kfree(Index_of);
520 return nb_errors;
521}
522
523EXPORT_SYMBOL_GPL(doc_decode_ecc);
524
525MODULE_LICENSE("GPL");
526MODULE_AUTHOR("Fabrice Bellard <fabrice.bellard@netgem.com>");
527MODULE_DESCRIPTION("ECC code for correcting errors detected by DiskOnChip 2000 and Millennium ECC hardware");